Page 909 - Advanced_Engineering_Mathematics o'neil
P. 909
Index 889
particular, 4–6 electrical circuits, applications for,
second-order equations, 44–45, 47–49 70–71
series, 121–135 equation for, 62
singular, 4 equilibrium position and, 61
systems, 106–110 forced, 66–67
transient term, 19–20 natural length L,61
trivial, 219 overdamping, 63
Sonine’s integral, 561 resonance, 67–69
Source term, heat equation, 619–622 second-order differential applications
Span, vector space, 165–166 for, 61–71
Spanning sets, 166–174 spring constant k,61
Spanning tree, 263 underdamping, 65–67
Special functions, 505–562, 799 unforced, 62–66
Bessel functions, 533–560, 799 Square matrix, 192
Bessel’s inequality, 515–518 Squares, Neumann problem for, 660
boundary conditions, 506 Standard representation of vectors, 151,
convergence of eigenfunction 165
expansion, 512–513 Stationary flow, 780
defined, 505 Steady-state, 19–20, 407, 655–658
eigenfunction expansions and, heat equation, 407
505–562 temperature distribution for a sphere,
gamma function (x), 533–534 655–658
Kepler’s problem, 556–560 value, 19–20
Legendre polynomials, 518–532, 799 Step size h, 139
MAPLE commands for, 799 Stereographic projection, 762–763
normalized eigenfunctions, 516 Stoke’s theorem, 402, 408–413
orthogonality of eigenfunctions, 511 boundary curves and, 408–409
Parseval’s theorem, 515–518 defined, 409
Sturm-Liouville problems, 506–515 Maxwell’s equations and, 411–413
weight function p, 511, 515 potential theory in 3-space using,
weighted dot product of, 515 410–411
Speed v(t), 349 surface analysis using, 402, 408–413
Spherical cylindrical coordinates, vector integral analysis using, 402,
415–416, 419–420 408–413
Spiral point, 335 Streamlines, 354–356, 783–784
Spiral sink, 335 fluid flow model graphs, 783–784
Spiral source, 335–336 3-space vectors, 354–356
Spring constant k,61 Sturm-Liouville problems, 506–515
Spring motion, 61–71 boundary conditions, 506
beat phenomena, 69–70 convergence of eigenfunction
critical damping, 63–64, 67 expansion, 512–513
damping constant c,61 differential equation, 506
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